Chain cross section

Data reported by Balta Calleja et al.17 > have, indeed, provided evidence for the nearly linear decrease of crystallite microhardness in PE with increasing chain cross-section in the crystalline phase. 

One may expect that with increasing temperature the thermal expansion in the crystalline regions will lead to an enlargement of the chain cross-section in the crystalline phase which in turn will induce a decrease in the cohesion energy of the crystals thus causing a gradually lower resistance to plastic deformation. In order to minimize the effect of the surface layer, the influence of temperature on microhardness has been investigated in PE crystallized at 260 °C under a pressure of 5 Kbar 28). The decrease of MH with temperature for the above chain extended PE material is depicted in Fig. 11. The hardness decrease follows an exponential law... 

Table 1. Comparison of hydrophilic polymers with various chain cross-sectional areas in formation of crystalline complexes with cyclodextrins...

So far, we have considered cross-section balance between one hydrophilic part and one hydrophobic part. We can also consider a different type of cross-section balance between one hydrophilic part and two hydrophobic parts. This is possible because the molecular area of CnAzoCmN+Br is almost equal to twice that of the chain cross-section. In this case, we will obtain a tilt angle of 23° from the relation of Sm cos0=2 Sc. This is another stable state of CnAzoCmN+Br, known as the interdigitated H-aggregation state which is observed in several compounds with m-ns2. 

There are two methods which have been used to date. In the first the force constants derived from IR and/or Raman data are substituted into expressions which give chain extension in terms of applied force. A chain modulus is then deduced by using an effective chain cross-sectional area. In the second method lattice dynamics is used to derive all the elastic constants for an infinite crystal. 

Crystals of most polar lipids can swell in the presence of water. The corresponding phases, gel-phases, with lamellarly packed lipid, and water layers, are sometimes thermodynamically stable (Larsson, 1994, p. 41). Also, the hydrocarbon chain packing of gel-phases usually show some axial rotational disorder. The alkyl chain cross-sectional area is close to 20 A2 in a plane perpendicular... 

One may attempt to derive the ideal shear strength So of the van der Waals solid normal to the chain axis from the value of the lateral surface free energy, a. This value is well known for common polymers such as PE or polystyrene (PS) (Hoffman et al, 1976) or else can be calculated from the Thomas-Stavely (1952) relationship a = /a Ahf)y, where a is the chain cross-section in the crystalline phase, Ahf is the heat of fusion, and y is a constant equal to 0.12. If one now assumes that a displacement between adjacent molecules by Si within the crystal is sufficient for lattice destruction then the ultimate transverse stress per chain will be given by So = cr/31. The values so obtained are shown in Table 2.1 for various polymers. In some cases (nylon, polyoxymethylene, polyoxyethylene (POE)) the agreement with experiment is fair. In the others, deviations are more evident. In order to understand better the discrepancy between the experimentally observed and the theoretically derived compressive strength one has to consider more thoroughly the micromorphology of polymer solids and the phenomena caused by the applied stress before lattice destruction occurs. 

T0 5 bar ). The main transition is accompanied by a well pronounced 3 % change in volume, which is mainly due to changes of the chain cross-sectional area, because chain disorder increases drastically at the transition. The volume change at the main transition decreases slightly with increasing temperature and pressure along the main transition line. 

In comparison with saturated chains containing the same number of carbon atoms, organic compounds possessing unsaturated chains exhibit a lower melting point, higher solubility, CMC, chemical activity, and larger chain cross-sectional area. This is shown in Table 5.13. Four factors that affect the solubility products of reagents with unsaturated chains are ... 

These general comments apply to some extent to all cold, "whole transfer wear processes. PTFE is unusual in that it transfer very readily in this type of process more so than any other known polymer. Further, the transfer films have particularly poor adhesion to most substrates and also have extremely high degrees of orientation. Some chain scission can be detected (38,42,50). They are also uncommonly thin sometimes no more than 10 nm in thickness (some workers believe they may be of the order of one molecular-chain cross section diameter in thickness, ca. 0.8 nm). 

Figure 11-7. Ratio Cil C of the Mooney-Rivlin constants of different elastomers as a function of the chain cross section for 2Ci = 0.2 MPa. (After R. F. Boyer and R. L. Miller.)...

Note that/(4)ocl/4 at the largest wave-vectors (l/4< /) since the chain is rigid and straight at these short length-scales, so its apparent fractal dimension df = 1 (the chain cross section is neglected here, it is assumed to be very thin). 

On the other hand, the mechanical properties also depend on the materials molecular composition and structure, i.e., intrinsic parameters. Intrinsic parameters are, for instance, chemical composition or constitution, configuration, conformation, chain cross section, entanglement molecular weight, free volume, chain stiffness, macromolecular mobility, crystallinity, and others [4, 16, 17]. Chain length and chain length distribution (or molecular weight M ) have a basic influence on mechanical properties, which is illustrated in Fig. 1.17. Three regions can be identified ... 

Figure 4.5 Scattering curve plotted by means of a Kratky plot for syndiotactic polystyrene in the SOL state. The fit is achieved with Yamakawa s pseudoanalytical equations and by considering a finite chain cross section, hence the departure from a linear variation at large q. Here, = 9nm and = 0.62 0.1 nm. Replotted from [50].

The onset point of the shear thinning effect of PE solution depends on the inverse of the relaxation time of the PE chain [152]. It is interesting to note that the shear thinning effects in the study of Krause were found only for high molecular weight samples, and therefore no exact relaxation time could be determined [152]. Generally, the trend of shear thinning can be explained by an extension of the PE chain by shear force, and the viscosity is proportional to the size of the chain cross section that is exposed to the flow, as defined by the Pincus blob size, and therefore t] [165]. This behavior was explained with a modified Rouse... 

Fig. 3.9. Critical tensile strength (strength at ductile-brittle transition) vs. chain cross-section (after Vincent [71]).

Here k is the constant of chain elasticity (not normalized with respect to the chain cross-section). 

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